In a large pot, combine chicken broth, ginger, and garlic. Bring to a gentle boil.
Add the chicken breasts and cook for 20–25 minutes until tender. Remove from the pot and shred using forks.
Soak mung bean noodles in warm water for 10–15 minutes until soft, then drain.
Return shredded chicken to the pot, add soy sauce and sesame oil, and simmer for another 5 minutes.
Stir in softened noodles and let them absorb the broth for 2–3 minutes.
Season with salt, pepper, and fish sauce if using.
Ladle the soup into bowls, garnish with green onions and cilantro, and serve warm.